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[2602.15632] Neural-POD: A Plug-and-Play Neural Operator Framework for Infinite-Dimensional Functional Nonlinear Proper Orthogonal Decomposition
Summary
The Neural-POD framework introduces a novel approach to constructing nonlinear orthogonal basis functions in infinite-dimensional spaces using neural networks, overcoming limitations of classical Proper Orthogonal Decomposition.
Why It Matters
This research addresses critical challenges in AI for science, particularly the issue of discretization in learned representations. By enabling resolution-invariant mappings and capturing nonlinear structures, Neural-POD enhances the applicability of reduced order modeling and operator learning, potentially transforming computational physics and machine learning applications.
Key Takeaways
- Neural-POD provides a plug-and-play framework for nonlinear basis function construction.
- It overcomes limitations of classical Proper Orthogonal Decomposition by allowing optimization in arbitrary norms.
- The framework generalizes effectively to unseen parameter regimes and captures complex nonlinear structures.
- Neural-POD integrates seamlessly with both reduced order modeling and deep operator learning frameworks.
- Demonstrated robustness across various complex spatiotemporal systems, including fluid dynamics equations.
Physics > Computational Physics arXiv:2602.15632 (physics) [Submitted on 17 Feb 2026] Title:Neural-POD: A Plug-and-Play Neural Operator Framework for Infinite-Dimensional Functional Nonlinear Proper Orthogonal Decomposition Authors:Changhong Mou, Binghang Lu, Guang Lin View a PDF of the paper titled Neural-POD: A Plug-and-Play Neural Operator Framework for Infinite-Dimensional Functional Nonlinear Proper Orthogonal Decomposition, by Changhong Mou and 2 other authors View PDF HTML (experimental) Abstract:The rapid development of AI for Science is often hindered by the "discretization", where learned representations remain restricted to the specific grids or resolutions used during training. We propose the Neural Proper Orthogonal Decomposition (Neural-POD), a plug-and-play neural operator framework that constructs nonlinear, orthogonal basis functions in infinite-dimensional space using neural networks. Unlike the classical Proper Orthogonal Decomposition (POD), which is limited to linear subspace approximations obtained through singular value decomposition (SVD), Neural-POD formulates basis construction as a sequence of residual minimization problems solved through neural network training. Each basis function is obtained by learning to represent the remaining structure in the data, following a process analogous to Gram--Schmidt orthogonalization. This neural formulation introduces several key advantages over classical POD: it enables optimization in arbitrary norms (e.g., ...